Technology can help persuade people to change their attitudes or behaviors. Elderly population is not familiar with information technology but e-Health services can help people maintain a healthy lifestyle. In order for the elderly to get benefits from e-Health services, they need to change their attitudes or behaviors. To make this change, it is necessary to persuade the elderly to embrace the use of smartphone. This research investigated factors that influence the elderly's intention to use e-Health services via a smartphone. According to the UTAUT model, the factors that influence the user's intention to use e-Health services are as follows: Performance Expectancy, Effort Expectancy, Social Influence, and Facilitating Conditions. Although the UTAUT model has been widely used to explain user acceptance and use of technology, lack of experience with recent technological advancement and age related deficiencies makes it less attractive for the elderly to adopt new technologies such as the smartphone. This is directly related to the elderly's perception of whether new technology can benefit to their lives. Hence, in this study, the UTAUT model has been extended to include a `Perceived Value' factor. The proposed model identified factors influencing the elderly's intention to use e-Health services via a smartphone. It is found that `Perceived Value' has a strong significance on the elderly's intention to use smartphone, followed by Facilitating Conditions and Effort Expectancy. In contrast, Performance Expectancy and Social Influence did not have a significant influence on intention. With the proposed model, it is possible to develop better e-Health services to meet the needs of the elderly based on widely available smartphones.